Question

1) You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sam, with mass 72.0 kg , is given a push and slides eastward. Abigail, with mass 60.0 kg , is sent sliding northward. They collide, and after the collision Sam is moving at 36.0 ∘ north of east with a speed of 6.20 m/s and Abigail is moving at 20.0 ∘ south of east with a speed of 9.40 m/s .

Part A

What was the speed of each person before the collision?
Sam's speed:

Part B

Abigail's speed:

Part C

By how much did the total kinetic energy of the two people decrease during the collision?

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2) A 21.00 kg lead sphere is hanging from a hook by a thin wire 4.00 m long, and is free to swing in a complete circle. Suddenly it is struck horizontally by a 6.00 kg steel dart that embeds itself in the lead sphere.

Part A

What must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision?

Answer 1

oblique

m1 (Sam) = 72 kg               m2 =(Abigail ) = 0.5 kg

befor collision

u1x = ?                  u2x = 0

u1y = 0                   u2y = ?

after collision

v1x = 6.2*cos36 = 5.01 m/s               v2x = 9.4*cos20 = 8.83 m/s

v1y = 6.2*sin36 = 3.64 m/s              v2y = -9.4*sin20 = -3.21 m/s

from momentum conservation

along x axis

Pix = Pfx

m1*u1x = m1*v1x + m2*v2x

72*u1x = 72*5.01 + 60*8.83

u1x = 12.4 m/s <<-------answer

along y

Piy = Pfy

60*u2y = 72*3.64 - 60*3.21

u1y = 1.16m/s <<---------------answer